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5^x + 5^3 * 5^(-x) = 30
5^x + 125 * 1/(5^x) = 30
5^x = t i t > 0
t + 125 * 1/t = 30 ------ / * t
t^2 + 125 = 30t
t^2 - 30t + 125 = 0
Δ = 900 - 500 = 400
√Δ = 20
t1 = (30 - 20) / 2 = 5
t2 = (30 + 20) / 2 = 25
5^x = 5 lub 5^x = 25
5^x = 5^1 lub 5^x = 5^2
x = 1 lub x = 2
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5^x + 5^3 * 5^(-x) = 30
5^x + 125 * 1/(5^x) = 30
5^x = t i t > 0
t + 125 * 1/t = 30 ------ / * t
t^2 + 125 = 30t
t^2 - 30t + 125 = 0
Δ = 900 - 500 = 400
√Δ = 20
t1 = (30 - 20) / 2 = 5
t2 = (30 + 20) / 2 = 25
5^x = 5 lub 5^x = 25
5^x = 5^1 lub 5^x = 5^2
x = 1 lub x = 2